Evaluation of the effect of equal power spectrum filtering in image restoration

The effectiveness of equal power spectrum filtering in image restoration is analyzed via digital simulation. We start with a gray-scale map of concentric rings with different grey values. To obtain a dirty image, the original image is first transformed via a linear space-invariant system. Then, white noise is mixed into the image. The equal power spectrum filter is then used for the image restoration. The signal to noise ratio (SNR) and a defined steepness of the steps, together with the visual impression, are accepted to characterize the performance of the image restoration. It is concluded that a satisfactory restoration can be realized when the SNR > 15. When SNR < 5, the image is completely un-restorable. The effect of system's transfer function on image restoration is also discussed. The effectiveness of the presented model of equal power spectrum filter is confirmed by applying it to the restoration of an actual astronomical image. Finally, a typical application of the equal power spectrum filter is given.